We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas w.r.t. the estimation of risk measures in risk management.

We study asset price bubbles in market models with proportional transaction costs $\lambda\in (0,1)$ and finite time horizon $T$ in the setting of [49]. By following [28], we define the fundamental value $F$ of a risky asset $S$ as the price of a super-replicating portfolio for a position terminating in one unit of the asset and zero cash. We then obtain a dual representation for the fundamental value by using the super-replication theorem of [50]. We say that an asset price has a bubble if its fundamental value differs from the ask-price $(1+\lambda)S$. We investigate the impact of transaction costs on asset price bubbles and show that our model intrinsically includes the birth of a bubble.

We suggest use continuous numerical risk grades [0,1] of R for a single risk or the unit cube in Rn for n risks as the economic domain. We consider risk ratings of economic agents as their coordinates in the economic domain. Economic activity of agents, economic or other factors change agents risk ratings and that cause motion of agents in the economic domain. Aggregations of variables and transactions of individual agents in small volume of economic domain establish the continuous economic media approximation that describes collective variables, transactions and their flows in the economic domain as functions of risk coordinates. Any economic variable A(t,x) defines mean risk XA(t) as risk weighted by economic variable A(t,x). Collective flows of economic variables in bounded economic domain fluctuate from secure to risky area and back. These fluctuations of flows cause time oscillations of macroeconomic variables A(t) and their mean risks XA(t) in economic domain and are the origin of any business and credit cycles. We derive equations that describe evolution of collective variables, transactions and their flows in the economic domain. As illustration we present simple self-consistent equations of supply-demand cycles that describe fluctuations of supply, demand and their mean risks.

We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity solutions linked to order book formation and recovery is explored. The main result is that order book recovery from aggressive liquidity taking follows a simple $t^{1/3}$ scaling law.

I analyze Osaka factory worker households in the early 1920s, whether idiosyncratic income shocks were shared efficiently, and which consumption categories were robust to shocks. While the null hypothesis of full risk-sharing of total expenditures was rejected, factory workers maintained their households, in that they paid for essential expenditures (rent, utilities, and commutation) during economic hardship. Additionally, children's education expenditures were possibly robust to idiosyncratic income shocks. The results suggest that temporary income is statistically significantly increased if disposable income drops due to idiosyncratic shocks. Historical documents suggest microfinancial lending and saving institutions helped mitigate risk-based vulnerabilities.

Do competent women receive unfavorable treatment than equally competent men? I study this question in a laboratory experiment where unfavorable treatment has material consequences. I find that neither men nor women treat competent women less favorably; if anything, both men and women treat competent women slightly more favorably than equally competent men. The findings provide a piece of evidence that competent women may not necessarily receive unfavorable treatment in settings with material consequences, which may shed new light on hiring and promotion practices in labor markets.

Technological advancement has lead to an increase in number and type of trading venues and diversification of goods traded. These changes have re-emphasized the importance of understanding the effects of market competition: does proliferation of trading venues and increased competition lead to dominance of a single market or coexistence of multiple markets? In this paper, we address these questions in a stylized model of Zero Intelligence traders who make repeated decisions at which of three available markets to trade. We analyse the model numerically and analytically and find that parameters that govern traders' decisions -- memory length and intensity of choice, e.g. how strongly decisions are based on past success -- make the key distinctions between consolidated and fragmented steady states of the population of traders. All three markets coexist with equal shares of traders only when either learning is too weak and traders choose randomly, or when markets are identical. In the latter case, the population of traders is fragmented across the markets. For the more general case of markets with different biases, we note that market dominance is the more typical scenario. These results are interesting because previously either strong differentiation of markets or heterogeneity in the needs of traders was found to be a necessary condition for market coexistence. We show that, in contrast, these states can emerge simply as a consequence of co-adaptation of an initially homogeneous population of traders.

Progress to-date towards the ambitious global 2030 agenda for sustainable development has been limited, and upheaval from the COVID-19 pandemic will further exacerbate the already significant challenges to Sustainable Development Goal (SDG) achievement. Here, we undertake a model-based global integrated assessment to characterise alternative pathways towards 36 time-bound, science-driven targets by 2030, 2050, and 2100. We show that it will be unlikely to jointly achieve socioeconomic and environmental targets by 2030, even under the most optimistic pathways and the least ambitious targets. Nonetheless, humanity can still avoid destabilisation of the Earth system and increase socioeconomic prosperity post-2030 via a Green Recovery pathway. A Green Recovery by mid- and end of the century requires reducing global population by 5% and 26%, empowering sustainable economic development by 32% and 52%, increasing education availability by 10% and 40%, reducing the total global fossil energy production by 36% and 80%, reducing agricultural land area by 7% and 10%, and promoting healthy and sustainable lifestyles by lowering consumption of animal-based foods (i.e., meat and dairy) by 39% and 50%, compared to the business-as-usual trajectories for 2050 and 2100, respectively. Our results show that the combination of these changes together towards extended, more ambitious goals by 2050 and 2100 is central to the transformative change needed to ensure that both people and planet prosper in medium- and long-term futures.

Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.

We study the problem of learning choice functions, which play an important role in various domains of application, most notably in the field of economics. Formally, a choice function is a mapping from sets to sets: Given a set of choice alternatives as input, a choice function identifies a subset of most preferred elements. Learning choice functions from suitable training data comes with a number of challenges. For example, the sets provided as input and the subsets produced as output can be of any size. Moreover, since the order in which alternatives are presented is irrelevant, a choice function should be symmetric. Perhaps most importantly, choice functions are naturally context-dependent, in the sense that the preference in favor of an alternative may depend on what other options are available. We formalize the problem of learning choice functions and present two general approaches based on two representations of context-dependent utility functions. Both approaches are instantiated by means of appropriate neural network architectures, and their performance is demonstrated on suitable benchmark tasks.

We study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in B\"auerle and Ott (2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital.

I study endogenous learning dynamics for people expecting systematic reversals from random sequences - the "gambler's fallacy." Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution's mean and stops too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. Subsidizing search partially mitigates long-run belief distortions.

In this paper, we are concerned with the valuation of Catastrophic Mortality Bonds and, in particular, we examine the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of assets. This bond was the first Catastrophic Mortality Bond to be launched in the market and encapsulates the behaviour of a well-defined mortality index to generate payoffs for bondholders. Pricing these type of bonds is a challenging task and no closed form solution exists in the literature. In our approach, we express the payoff of such a bond in terms of the payoff of an Asian put option and present a new approach to derive model-independent bounds exploiting comonotonic theory as illustrated in \cite{prime1}, \cite{2} and \cite{Simon} for the pricing of Asian options. We carry out Monte Carlo simulations to estimate the bond price and illustrate the quality of the bounds.

We consider the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it. Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lies within a Wasserstein ball surrounding it. The investor then chooses the alternative strategy that minimises their personal risk preferences, modelled in terms of a distortion risk measure. In a general market model, we prove that an optimal dynamic strategy exists and is unique, and provide its characterisation through the notion of isotonic projections. Finally, we illustrate how investors with different risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped distortion risk measures, and lower- and upper-tail risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving some aspects of the benchmark.

Research on quantum technology spans multiple disciplines: physics, computer science, engineering, and mathematics. The objective of this manuscript is to provide an accessible introduction to this emerging field for economists that is centered around quantum computing and quantum money. We proceed in three steps. First, we discuss basic concepts in quantum computing and quantum communication, assuming knowledge of linear algebra and statistics, but not of computer science or physics. This covers fundamental topics, such as qubits, superposition, entanglement, quantum circuits, oracles, and the no-cloning theorem. Second, we provide an overview of quantum money, an early invention of the quantum communication literature that has recently been partially implemented in an experimental setting. One form of quantum money offers the privacy and anonymity of physical cash, the option to transact without the involvement of a third party, and the efficiency and convenience of a debit card payment. Such features cannot be achieved in combination with any other form of money. Finally, we review all existing quantum speedups that have been identified for algorithms used to solve and estimate economic models. This includes function approximation, linear systems analysis, Monte Carlo simulation, matrix inversion, principal component analysis, linear regression, interpolation, numerical differentiation, and true random number generation. We also discuss the difficulty of achieving quantum speedups and comment on common misconceptions about what is achievable with quantum computing.

We propose the Hawkes flocking model that assesses systemic risk in high-frequency processes at the two perspectives -- endogeneity and interactivity. We examine the futures markets of WTI crude oil and gasoline for the past decade, and perform a comparative analysis with conditional value-at-risk as a benchmark measure. In terms of high-frequency structure, we derive the empirical findings. The endogenous systemic risk in WTI was significantly higher than that in gasoline, and the level at which gasoline affects WTI was constantly higher than in the opposite case. Moreover, although the relative influence's degree was asymmetric, its difference has gradually reduced.

This paper develops a methodology for tracking in real time the impact of shocks (such as natural disasters, financial crises or pandemics) on gross domestic product (GDP) by analyzing high-frequency electricity market data. As an illustration, we estimate the GDP loss caused by COVID-19 in twelve European countries during the first wave of the pandemic. Our results are almost indistinguishable from the official statistics of the recession during the first two quarters of 2020 (correlation coefficient of 0.98) and are validated by several robustness tests. However, they are also more chronologically disaggregated and up-to-date than standard macroeconomic indicators and, therefore, can provide crucial and timely information for policy evaluation. Our results show that delaying intervention and pursuing 'herd immunity' have not been successful strategies so far, since they increased both economic disruption and mortality. We also find that coordinating policies internationally is fundamental for minimizing spillover effects from NPIs across countries.